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To multiply the complex numbers \((-10 + 5i)\) and \((-10 - 5i)\), we can use the formula for multiplying two binomials, which is similar to the distributive property (also known as the FOIL method):

\[ (a + b)(c + d) = ac + ad + bc + bd \]

For our specific case:

• \(a = -10\)
• \(b = 5i\)
• \(c = -10\)
• \(d = -5i\)

Now, we multiply:

\[ (-10 + 5i)(-10 - 5i) = (-10)(-10) + (-10)(-5i) + (5i)(-10) + (5i)(-5i) \]

Calculating each term:

1. \((-10)(-10) = 100\)
2. \((-10)(-5i) = 50i\)
3. \((5i)(-10) = -50i\)
4. \((5i)(-5i) = -25i^2\)

Now, substitute \(i^2 = -1\):

\(-25i^2 = -25(-1) = 25\)

Now, combine all the terms:

\[ 100 + 50i - 50i + 25 = 100 + 25 = 125 \]

So, the final result of \((-10 + 5i)(-10 - 5i)\) is:

\(\boxed{125}\)